Two options by the looks of things here, either you get brand new matching RAM to see if that solves the problem or you get a new internal drive if you think it is that, that has gone bad. You can use the following guide I have written for you to clone your internal drive to a new external HDD as well if you feel the need to do so.
Best bet is to get a new internal drive with a 2.5" USB enclosure, use the same method of booting into the install disk and going into Disk Utility, on the left pane select you hdd then click the Restore tab, drag your internal drive from the left pane into the "Source" field then drag your new internal drive via USB from the left pane into the "Destination" field then click restore. This will copy your entire internal drive to the your new internal via USB. You can then swap the old internal for the new internal and see if that has solved the problem.

Hope this helps

- Simon

I am a bit confused. Am I right in thinking that form what you have just told me, I can plug in my external hard drive, and it will show up on disk utility, allowing me to literally drag Macintosh HD into the external hard drive and everything will go onto the external?
and do you mean internal as in a whole new hard drive for my mac?
Sorry if I am sounding stupid!